Simplify the following expression: $ n = \dfrac{1}{7} - \dfrac{k - 1}{k - 4} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{k - 4}{k - 4}$ $ \dfrac{1}{7} \times \dfrac{k - 4}{k - 4} = \dfrac{k - 4}{7k - 28} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{k - 1}{k - 4} \times \dfrac{7}{7} = \dfrac{7k - 7}{7k - 28} $ Therefore $ n = \dfrac{k - 4}{7k - 28} - \dfrac{7k - 7}{7k - 28} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{k - 4 - (7k - 7) }{7k - 28} $ Distribute the negative sign: $n = \dfrac{k - 4 - 7k + 7}{7k - 28}$ $n = \dfrac{-6k + 3}{7k - 28}$